The cup product of Brooks quasimorphisms

TL;DR

This paper demonstrates that the cup product of bounded cohomology classes from Brooks quasimorphisms on free groups always vanishes, linking it to the vanishing of a universal class in tree automorphism groups.

Contribution

It establishes the universal vanishing of the cup product for classes from Brooks quasimorphisms, revealing new structural properties of bounded cohomology.

Findings

Cup product of Brooks quasimorphisms' classes vanishes

Square of a universal class for tree automorphism groups vanishes

Provides insight into the structure of bounded cohomology in free groups

Abstract

We prove the vanishing of the cup product of the bounded cohomology classes associated to any two Brooks quasimorphisms on the free group. This is a consequence of the vanishing of the square of a universal class for tree automorphism groups.